Semidomains and Metabelian Product of Metabelian Lie Algebras

This article is the fourth part of the series of papers whose aim is the construction of algebraic geometry over metabelian Lie algebras. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 14, Algebra, 2004.     

On characterization of Poisson and Jacobi structures

We characterize Poisson and Jacobi structures by means of complete lifts of the corresponding tensors: the lifts have to be related to canonical structures by morphisms of corresponding vector bundles. Similar results hold for generalized Poisson and Jacobi structures (canonical structures) associated with Lie algebroids and Jacobi algebroids.     

Load-Carrying Capacity of Circular Plates Made of a Fiber-Reinforced Composite

The load-carrying capacity of circular plates made of a fiber-reinforced composite and loaded with axisymmetric transverse forces under axisymmetric boundary conditions is investigated. The plates can be freely supported or clamped along their contour. To the known yield condition used, in the plane of main bending moments, there correspond irregular hexagons, which depend on the mechanical properties of composite constituents and some characteristic geometrical parameters. It is shown that, depending on the ratio of ultimate radial and circumferential bending moments, in the plastic state, the circular plates (the central part of the clamped plates) take the form of a cone or a frustum of cone. For each of the cases, the limit load is found, which is a function of the above-mentioned mechanical parameters. The statically allowable fields of bending moments and the corresponding allowable fields of deflection rates are determined. The solutions found are exact. Special cases for the freely supported plates are analyzed, and the results obtained are presented in the form of graphs.__________Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 2, pp. 177–192, March–April, 2005.     

Structure of luminous clouds near a sublimated hydrogen pellet

The spatial structure of a luminous cloud near a hydrogen pellet sublimated in a tokamak plasma is investigated experimentally. The luminous cloud has the form of a constant-intensity plateau extended along the magnetic field and is surrounded by an exponentially fading halo. The cross size of the plateau is determined by the boundary of the ionization region of atoms leaving the pellet surface. The plateau length is approximately determined by the balance between the pressures in the luminous cloud and the bulk plasma. Taking into account the structure described is important for the correct interpretation of the signals from alpha-particle diagnostics by charge-exchange neutral fluxes, because these signals depend on the characteristic dimensions of the cloud.     

Comparison of XYZ Model Fitting Functions for 111Cd in In3La

The XYZ model describes the interaction between nuclear probes and an electric field gradient that fluctuates among three orthogonal directions. The model presents a means to calculate the perturbation function that represents spectra obtained using perturbed angular correlation spectroscopy. Three analytic approximations of the perturbation function have been developed previously, and they are evaluated in the present paper in the context of Cd jumping among In-lattice sites in In₃La.     

An experimental analysis of a population based approach for global optimization

In this paper we perform a computational analysis of a population based approach for global optimization, Population Basin Hopping (PBH), which was proven to be very efficient on very challenging global optimization problems by the authors (see ). The experimental analysis aims at understanding more deeply how the approach works and why it is successful on challenging problems.     

Photon production in a dense medium

On the basis of diagram formalism for two-particle Green functions, the bremsstrahlung of charged particles interacting in a dense medium is investigated. In the case of production of soft photons, exact expressions for two-particle Green functions corresponding to the process of particle bremsstrahlung in the substance are obtained. The Green functions found are fully determined by the set of closed irreducible diagrams. It is shown that, in the case of radiation in a sufficiently dense medium in a far long-wave region of the spectrum, the coherent multiple particle scattering results in an additional (as compared that reported earlier in [1–13]) suppression of the bremsstrahlung photon yield.     

Damping of coupled phonon-plasmon modes

The effect of free carriers on the dispersion and damping of coupled phonon-plasmon modes is considered in the long-wave approximation. The electron and phonon scattering rate, as well as Landau damping, is taken into account.